| EPSRC Reference: |
EP/N023919/1 |
| Title: |
Cherednik Algebras and Affine Lie Algebras |
| Principal Investigator: |
Nazarov, Professor M |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
University of York |
| Scheme: |
Standard Research |
| Starts: |
01 October 2016 |
Ends: |
31 March 2019 |
Value (£): |
193,805
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
Representation Theory was born about 120 years ago by blending ideas from Algebra, Analysis, Geometry and Number Theory, with motivations coming from the then contemporary Physics. It keeps a central position in Mathematics to this day, and has found numerous applications in Biology, Chemistry, Information Technology and especially in Theoretical Physics. For instance, it was Representation Theory that gave mathematical foundations to the celebrated prediction made in 1964 by P. Higgs (Nobel Prize 2013) and confirmed by CERN experimenters in 2012.
Reciprocally, Physics also remains a major source of inspiration for Representation Theory. This is particularly relevant to the present project, which is aimed to study certain algebraic objects emerged from the Theory of Integrable Systems and from the Quantum Field Theory. These algebraic objects were discovered around 1992 by I. Cherednik, who then used them to prove the famous conjectures of I. Macdonald on multivariate orthogonal polynomials. Since then these algebras have become the focus of attention of many world leading mathematicians, and found striking applications in Algebraic Geometry, Combinatorics and Mathematical Physics. We aim to advance the theory of these algebras by using the methods coming from the theory of affine Lie algebras.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.york.ac.uk |